** Answers without relevant diagrams/circuits wherever necessary will not carry any marks

PART-A

I. Answer all the following questions (1×5)

1. Where would Coulomb’s interaction be weaker in dielectric medium or vacuum?

2. Between dipole and a point charge whose Electric Potential reduces faster?

3. What is the work done when a charge makes a rectangular path on an equi-potential surface?

4. Write the de-Broglie formula for wavelength of a wave-particle if its momentum is p?

5. Define refractive index from angle of incidence and angle of reflection.

PART-B

II. Answer any Five of the following questions, 2 marks each. (2×5=10)

6. State how density of electric lines of force is related to the Electric Field Vector intensity E. Also mention another property of the lines of forces and one property of the equipotential surface.

7. Write the Gauss law of electrostatics and define Electric Flux for a uniform field E.

8. How one defines the direction of a Dipole Vector? What’s the potential vertical to the dipole axis?

9. What’s the energy of an electron if we place it in a potential difference of 100 Volt assuming its at rest at this location? What will be the energy of an alpha-particle if its placed at the same location at rest.

10. Define atomic number and atomic mass unit.

11. Write out the expression of n-th level atomic spectra {energy level} of a Hydrogen atom. What energy will be released if the electron jumps from level=5 to level = 3. ?

12. Write out the mirror equation. If an image is at 10 cm and object at 100 cm what’s the focal length of the mirror?

13. If angle of incidence is 450and angle of refraction is 300 what will be the refractive index of the medium?

PART-C

III. Answer any one of the following questions (5×1)

14. Derive the Electric Field Vector E||for the Dipole VectorP in a direction of alignment with the Dipole Vector, also called End-On configuration.

15.Derive the scalar potential V(r) in a general direction at angle J to the Dipole.

IV. Answer any two of the following questions (5×2)

16. Define Electric flux F (Phi) in 1 or 2 lines and write out expression for it for a uniform and non-uniform electric field E. State Gauss Law in terms of charge and flux in differential and integral form. State the vector form of Coulomb’s law of electrostatics force. What’s the flux of a vector if it is aligned to the area vector?

17. Define Lines of force and flux of a vector. State Gauss law and derive its mathematical form by considering spherical symmetry.

18. Obtain an expression for the Nuclear Size of an atom by solving for distance of closest approach (r). Use an incoming alpha-particle of mass mα and charge q that’s deflected by the presence of a nucleus of atomic number Z to obtain r. Now replace the variables by some numerical: mα = 6.8×10-27kg, e = 1.6 x 10-19 coul, Z=100, and vα= 1.0×107 m/s. Express the answer in Femto-meters.

V. Answer any three of the following questions (5×3)

19. A proton has a radius R and the charge Q is uniformly distributed. Use Bohr’s atomic energy level formula for the 1st excited state {n=2} and ground state (n=1) to obtain energy of the Hydrogen-atom.

20. State the power of a lens and thin lens formula. For thin lens case determine the focal length if the object distance is 100 cm and image distance is 25 cm.

21. Draw a simple and neat diagram showing a convex lens, optical center and focal point {Focus}. Now define power of a lens and obtain an expression for it.

22. Write the expression for the Electrostatics Potential of a point charge. Calculate the potential for a Nitrogen nucleus at a distance of 1 femto-meter (1 fm = 10-15 meters) {Z nitrogen=14}. Also do this for N=10.

V. Answer the following questions (5×1)

23. Following readings were obtained in one experiment you have performed to determine the focal length of a convex lens by u-v method. Follow the data in the table, u, v, x, y and plot the graph between x and y and obtain the slope S. Then determine the focal length from the slope.

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